Probabilistic forecasting: prediction intervals and prediction distribution¶

When trying to anticipate future values, most forecasting models focus on predicting the most likely value, which is called point-forecasting. Although knowing the expected value of a time series is useful for most business cases, this type of forecasting does not provide any information about the model's confidence or the prediction's uncertainty.

Probabilistic forecasting, as opposed to point-forecasting, is a family of techniques that enable the prediction of the expected distribution of the outcome, rather than a single future value. This type of forecasting provides much richer information, as it reports the range of probable values into which the true value may fall, allowing the estimation of prediction intervals.

A prediction interval is the interval within which the true value of the response variable is expected to be found with a given probability. There are multiple ways to estimate prediction intervals, most of which require that the residuals (errors) of the model follow a normal distribution. However, when this assumption cannot be made, two commonly used alternatives are bootstrapping and quantile regression.

To illustrate how skforecast enables the estimation of prediction intervals for multi-step forecasting, examples attempting to predict energy demand for a 7-day horizon are provided. Two strategies are showcased:

• Prediction intervals based on bootstrapped residuals.

• Prediction intervals based on quantile regression.